Tính nhanh
1×2+2×3+3×4+...+19×2
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\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{18.19}+\frac{2}{19.20}\)
\(=2\cdot\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\cdot\left(1-\frac{1}{20}\right)\)
\(=2\cdot\frac{19}{20}=\frac{19}{10}\)
\(D=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{20}=\dfrac{1}{2}-\dfrac{1}{20}=\dfrac{9}{20}\)
\(E=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{98\cdot99}\right)\)
\(=\dfrac{1}{99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{98}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{99}-1+\dfrac{1}{99}=\dfrac{2}{99}-1=-\dfrac{97}{99}\)
b: \(B=\dfrac{5}{2}-\dfrac{7}{2}+\dfrac{3}{8}+\dfrac{6}{8}+\dfrac{-6}{11}-\dfrac{5}{11}=-2-1+\dfrac{9}{8}=\dfrac{9}{8}-3=-\dfrac{15}{8}\)
c: \(C=\left(\dfrac{4}{3}+\dfrac{7}{3}+\dfrac{1}{3}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=4+1=5\)
d: \(D=\dfrac{4}{19}\left(\dfrac{-5}{6}-\dfrac{7}{12}\right)-\dfrac{40}{57}\)
\(=\dfrac{4}{19}\cdot\dfrac{-17}{12}-\dfrac{40}{57}=-1\)
e: \(E=\dfrac{1}{3}\left(\dfrac{4}{5}-\dfrac{9}{5}\right)+\dfrac{2}{3}=\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}\)
S = 1.2 + 2.3 + 3.4 + ......... + 19.20
3S = 1.2.3 + 2.3.3 + 3.4.3 + ....... + 19.20.3
3S=1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) +......+19.20.(21-18)
3S=1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4+........+19.20.21 - 18.19.20
3S=19.20.21
S = (19.20.21) : 3
S = 2660
Vậy S = 2660
^-^ Chúc bạn làm tốt !
A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 19 x 20
=> 3A = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 x ( 5 - 2 ) + ... + 19 x 20 x ( 21 - 18 )
=> 3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + .... + 19 x 20 x 21 - 18 x 19 x 20
=> 3A = 19 x 20 x 21
=> A = 19 x 20 x 7
Vậy A = 19 x 20 x 7
Đặt biểu thức là A
\(3xA=1x2x3+2x3x3+3x4x3+...+19x20x3=\)
\(=1x2x3+2x3\left(4-1\right)+3x4x\left(5-2\right)+...+19x20x\left(21-18\right)=\)
\(=1x2x3-1x2x3+2x3x4-2x3x4+3x4x5-...-18x19x20+19x20x21=\)
\(=19x20x21\Rightarrow A=\dfrac{19x20x21}{3}=7x19x20\)
1x2+2x3+3x4+......+19x20
đặt biểu thức là M
Gấp M lên 3 lần ta có:
M x 3 = 1x2x3 + 2x3x3 + 3x4x3 + … + 19x20x3
M x 3 = 1x2x3 + 2x3x(4 - 1) + 3x4x( 5 - 2) + … + 19x20x(21-18)
M x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + … + 19x20x21- 18x19x20
M x 3 = 19x20x21
M = 19x20x21:3=19x20x7=2660